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NASA NTRS2019

Bayesian Estimation of Earth’s Undiscovered Mineralogical Diversity Using Noninformative Priors

Recently, statistical distributions have been explored to provide estimates of the mineralogical diversity of Earth, and Earth-like planets. In this paper, a Bayesian approach is introduced to estimate Earth’s undiscovered mineralogical diversity. Samples are generated from a posterior distribution of the model parameters using Markov chain Monte Carlo simulations such that estimates and inference are directly obtained. It was previously shown that the mineral species frequency distribution conforms to a generalized inverse Gauss–Poisson (GIGP) large number of rare events model. Even though the model fit was good, the population size estimate obtained by using this model was found to be unreasonably low by mineralogists. In this paper, several zero-truncated, mixed Poisson distributions are fitted and compared, where the Poisson-lognormal distribution is found to provide the best fit. Subsequently, the population size estimates obtained by Bayesian methods are compared to the empirical Bayes estimates. Species accumulation curves are constructed and employed to estimate the population size as a function of sampling size. Finally, the relative abundances, and hence the occurrence probabilities of species in a random sample, are calculated numerically for all mineral species in Earth’s crust using the Poisson-lognormal distribution. These calculations are connected and compared to the calculations obtained in a previous paper using the GIGP model for which mineralogical criteria of an Earth-like planet were given.

Bayesian statistics↗

DOE OSTI2020

Worldwide Population Estimates for Small Geographic Areas

This chapter discusses the basis for these population estimates, scope, and limitations based on experiences in development of massive global population datasets and usage of these datasets as a basis for sampling design. It presents tools and approaches for using these georeferenced population estimates for complex household survey sampling. The chapter provides a unified resource for understanding current gridded population datasets, their use in survey research, and promising areas of future work toward improved population estimates. It includes an overview of popular gridded population datasets, common methodological frameworks for developing gridded population estimates, and discusses pros and cons for selecting a gridded population dataset from a survey perspective. The chapter focuses on survey methods that use gridded population estimates specifically. It highlights differences between census population estimates and gridded population estimates that may be relevant when planning data collection. The chapter presents a case study of gridded population data and sampling methods in Nigeria.

Amer, Safaa↗

DOE OSTI2020

In Search of a Cost-Effective Approach for Estimating Dam Passage Survival

Abstract Passage of downstream-migrating fishes through hydropower dams poses a management issue in rivers throughout the world. As such, regulations have been enacted at many locales to understand and limit fish losses by requiring dam passage survival estimation. However, limiting estimates of survival to the dam and immediate tailrace presents a challenge to researchers. In this study, two alternative release–recapture methods were used to estimate dam passage survival of juvenile salmonids through Lower Granite Dam on the Snake River, Washington, in 2018. One approach, the virtual/paired-release (ViPRe) model, was extensively used in the Columbia–Snake River basin at federally operated hydroelectric dams during 2010–2014. This existing approach uses three releases of tagged smolts to isolate dam passage survival, defined as survival from the upstream dam face to the tailrace mixing zone 1–2 km downstream of the dam. An alternative approach, the virtual release/dead-fish correction (ViRDCt) model, uses one live-release group paired with a release of dead tagged fish at the dam to estimate the same survival parameter. The alternative estimation approaches were tested on two spring out-migrating stocks, yearling Chinook Salmon Oncorhynchus tshawytscha and steelhead Oncorhynchus mykiss, and on a summer out-migrating stock of subyearling Chinook Salmon. The alternative estimates for these stocks were all within 1 SE. However, the ViRDCt model produced survival estimates with SEs that were 59% smaller than those of the existing ViPRe model and did so using 42% fewer tagged fish and one less downstream acoustic detection array. Because of the reduced sample size, nearly US$540,000 less in tag costs and 4,000 fewer labor-hours were required to implement the ViRDCt model compared to the ViPRe model. As such, the ViRDCt model represents a cost-effective and precise approach to characterizing dam passage survival.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

DART-PFLOTRAN: An ensemble-based data assimilation system for estimating subsurface flow and transport model parameters

Ensemble-based Data Assimilation (EDA), based on the Monte Carlo approach, has been effectively applied to estimate model parameters through inverse modeling in subsurface flow and transport problems. However, implementation of EDA approach involves a complicated workflow that include setting up and executing ensemble forward model simulations, processing observations and model simulation results for parameter updates, and repeat for sequential or iterative EDA. To facilitate the management of such workflow and lower the barriers for adopting EDA-based parameter estimation in subsurface science, we develop a generic software frame-work linking the Data Assimilation Research Testbed (DART) with a massively parallel subsurface FLOw and TRANsport code PFLOTRAN. The new DART-PFLOTRAN leverages both the core data assimilation engines in DART and the computational power afforded by PFLOTRAN. In addition to the standard smoother and filtering options, DART-PFLOTRAN enables an iterative EDA workflow based on the Ensemble Smoother for Multiple Data Assimilation method (ES-MDA) to improve estimation accuracy for nonlinear forward problems. Here, we verify the implementation of ES-MDA in DART-PFLOTRAN using two synthetic cases designed to estimate static permeability and dynamic exchange fluxes across the riverbed, respectively, from continuous temperature measurements made across a depth profile. One-dimensional hydro-thermal simulations are performed in both cases to relate temperature responses with the parameters of interest. In the case of estimating dynamic parameters, we demonstrate the flexibility of DART-PFLOTRAN in automating sequential ES-MDA workflow, which will significantly reduce the time researchers spend on managing complex workflows in similar applications. Both studies yield accurate estimations of the parameters compared to their synthetic truth, while ES-MDA leads to more accurate estimation when a high level of nonlinearity exist between observed responses and unknown parameters. With a code base in Python and Fortran, DART-PFLOTRAN paves the way for applications in large-scale subsurface inverse modeling by automating the complex workflow of sequential ES-MDA that can be executed on various computing platforms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Parametric estimation of Poisson's ratio for thin hinged-hinged plates

Cornu's method is an elegant calculation besieged by an impractical approach to obtain accurate estimates for Poisson's ratio. Conventionally, Cornu's method requires several components, and each component can adversely affect the accuracy of the measurement. Furthermore, Cornu's conventional method requires a long beam because beams with short length-to-width ratios cause the estimate of Poisson's ratio to diverge from the true value of Poisson's ratio. We believe that, with the right modifications, Cornu's method can become an attractive approach to obtaining precise estimates for Poisson's ratio from mode shapes. Here we use finite element simulations to show how to use Cornu's method to estimate Poisson's ratio from a mode shape. Our modified Cornu's method removes knife-edges and loading components for a hinged-hinged plate under steady-state excitation. Given the true value of Poisson's ratio, as a performance specification, we show that simple parametric expressions can fit estimates for Poisson's ratio for different length-to-width ratios of thin hinged-hinged plates. Additionally, we show that estimates for Poisson's ratio from higher modes align with the results from the first mode and explain our expectation for this outcome. Furthermore, our results challenge the idea that anticlastic, monoclastic, and synclastic deformation uniquely correspond to positive, zero, and negative estimates of Poisson's ratio, respectively. With the emergence of materials-by-design, we expect that this parametric technique will be able to assist in experimental qualification of thin beam and plate structures with respect to the desired value of Poisson's ratio.

42 ENGINEERING↗

DOE OSTI2023

Uncertainty quantification of the convolutional neural networks on permeability estimation from micro-CT scanned sandstone and carbonate rock images

Rock permeability is one of the most crucial properties affecting subsurface fluid flow behaviors. To accurately and robustly estimate the permeability, Digital Rock Physics, including micro-CT scanning technology and direct flow simulations on scanned images, has prevailed in recent years. Besides, machine learning techniques such as convolutional neural networks (CNNs) have been widely adopted and achieved success in permeability estimations directly from rock images. However, existing ML methods used for permeability estimation from rock images lack uncertainty quantification that causes unreliable predictions and overconfident estimations on out-of-distribution (OOD) samples. Here, in this work, we propose a PI3NN-CNN framework to address this problem. PI3NN-CNN consists of a CNN model for absolute permeability estimation and a PI3NN method to quantify the estimation uncertainty. It is able to quantify the uncertainty for in-distribution (InD) data with a desired confidence level, and identify OOD samples to avoid overconfident predictions. We demonstrate the method using micro-CT scanned images from two sandstone and two carbonate rocks. We found that PI3NN-CNN generates accurate predictions for InD samples, while producing high-quality prediction uncertainties regardless of the prediction accuracy. Meanwhile, PI3NN-CNN identifies OOD samples using its special network initialization scheme. The unique feature of PI3NN-CNN makes it applicable to more complex real-world image-based data for robust learning and predictions without overconfident estimations when the ground-truth information is unavailable.

58 GEOSCIENCES↗

DOE OSTI2023

Combining Remotely Sensed Evapotranspiration and an Agroecosystem Model to Estimate Center‐Pivot Irrigation Water Use at High Spatio‐Temporal Resolution

Abstract Estimating irrigation water use accurately is critical for sustainable irrigation and studying terrestrial water cycle in irrigated croplands. However, irrigation is not monitored in most places, and current estimations of irrigation water use has coarse spatial and/or temporal resolutions. This study aims to estimate irrigation water use at the daily and field scale through the proposed model‐data fusion framework, which is achieved by particle filtering with two configurations (concurrent, CON, and sequential, SEQ) by assimilating satellite‐based evapotranspiration (ET) observations into an advanced agroecosystem model, ecosys . Two types of experiments using synthetic and real ET observations were conducted to study the efficacy of the proposed framework for estimating irrigation water use at the irrigated fields in eastern and western Nebraska, United States. The experiments using synthetic ET observations indicated that, for two major sources of uncertainties of ET difference between observations and model simulations, which are bias and noise, noise had larger impacts on degrading the estimation performance of irrigation water use than bias. For the experiments using real ET observations, monthly and annual estimations of irrigation water use matched well with farmer irrigation records, with Pearson correlation coefficient ( r ) around 0.80 and 0.50, respectively. Although detecting daily irrigation records was very challenging, our method still gave a good performance with RMSE, BIAS, and r around 2.90, 0.03, and 0.4 mm/d, respectively. Our proposed model‐data fusion framework for estimating irrigation water use at high spatio‐temporal resolution could contribute to regional water management, sustainable irrigation, and better tracking terrestrial water cycle.

Environmental Sciences & Ecology↗

DOE OSTI2026

DESI DR1 Ly α 1D power spectrum: Validation of estimators

The Data Release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI) is the largest sample to date for small-scale Lyα forest cosmology, accessed through its one-dimensional power spectrum (P 1D ). The Lyα forest P 1D is extracted from quasar spectra that are highly inhomogeneous (both in wavelength and between quasars) in noise properties due to intrinsic properties of the quasar, atmospheric and astrophysical contamination, and also sensitive to low-level details of the spectral extraction pipeline. We employ two estimators in DR1 analysis to measure P 1D : the optimal estimator and the fast Fourier transform (FFT) estimator. To ensure robustness of our DR1 measurements, we validate these two power spectrum and covariance matrix estimation methodologies against the challenging aspects of the data. First, using a set of 20 synthetic 1D realizations of DR1, we derive the masking bias corrections needed for the FFT estimator and the continuum fitting bias needed for both estimators. We demonstrate that both estimators, including their covariances, are unbiased with these corrections using the Kolmogorov-Smirnov test. Second, we substantially extend our previous suite of CCD image simulations to include 675,000 quasars, allowing us to accurately quantify the pipeline's performance. This set of simulations reveals biases at the highest k values, corresponding to a resolution error of a few percent. We base the resolution systematics error budget of DR1 P 1D on these values, but do not derive corrections from them since the simulation fidelity is insufficient for precise corrections.

Lyman alpha forest↗

DOE OSTI2022

Local Group timing argument and virial theorem mass estimators from cosmological simulations

ABSTRACT We identify Local Group (LG) analogues in the IllustrisTNG cosmological simulation, and use these to study two-mass estimators for the LG: One based on the timing argument (TA) and one based on the virial theorem (VT). Including updated measurements of the Milky Way-M31 tangential velocity and the cosmological constant, we show that the TA mass estimator slightly overestimates the true median LG-mass, though the ratio of the TA to the true mass is consistent at the approximate 90 per cent c.l.. These are in broad agreement with previous results using dark matter-only simulations. We show that the VT estimator better estimates the true LG-mass, though there is a larger scatter in the virial mass to true mass ratio relative to the corresponding ratio for the TA. We attribute the broader scatter in the VT estimator to several factors, including the predominantly radial orbits for LG satellite galaxies, which differs from the VT assumption of isotropic orbits. With the systematic uncertainties we derive, the updated measurements of the LG mass at 90 per cent c.l. are $4.75_{-2.41}^{+2.22} \times 10^{12}$ M⊙ from the TA and $2.0_{-1.5}^{+2.1} \times 10^{12}$ M⊙ from the VT. We consider the LMC’s effect on the TA and VT LG mass estimates, and do not find exact LMC–MW–M31 analogues in the Illustris simulations. However, in LG simulations with satellite companions as massive as the LMC, we find that the effect on the TA and VT estimators is small, though we need further studies on a larger sample of LMC–MW–M31 systems to confirm these results.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Accurate shear estimation with fourth-order moments

ABSTRACT As imaging surveys progress in exploring the large-scale structure of the Universe through the use of weak gravitational lensing, achieving sub-per cent accuracy in estimating shape distortions caused by lensing, or shear, is imperative for precision cosmology. In this paper, we extend the Fourier power function shapelets (FPFS) shear estimator using fourth-order shapelet moments and combine it with the original second-order shear estimator to reduce galaxy shape noise. We calibrate this novel shear estimator analytically to a sub-per cent level-accuracy using the AnaCal framework. This higher order shear estimator is tested with realistic image simulations, and after analytical correction for the detection/selection bias and noise bias, the multiplicative shear bias $|m|$ is below $3\times 10^{-3}$ (99.7 per cent confidence interval) for both isolated and blended galaxies. Once combined with the second-order FPFS shear estimator, the shape noise is reduced by $\sim 35~{{\ \rm per\ cent}}$ for isolated galaxies in simulations with Hyper Suprime-Cam and Vera C. Rubin Observatory Legacy Survey of Space and Time observational conditions. However, for blended galaxies, the effective number density does not significantly improve with the combination of the two estimators. Based on these results, we recommend exploration of how this framework can further reduce the systematic uncertainties in shear due to point spread function leakage and modelling error, and potentially provide improved precision in shear inference in high-resolution space-based images.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Bootstrapping outperforms community‐weighted approaches for estimating the shapes of phenotypic distributions

Abstract Estimating phenotypic distributions of populations and communities is central to many questions in ecology and evolution. These distributions can be characterized by their moments (mean, variance, skewness and kurtosis) or diversity metrics (e.g. functional richness). Typically, such moments and metrics are calculated using community‐weighted approaches (e.g. abundance‐weighted mean). We propose an alternative bootstrapping approach that allows flexibility in trait sampling and explicit incorporation of intraspecific variation, and show that this approach significantly improves estimation while allowing us to quantify uncertainty. We assess the performance of different approaches for estimating the moments of trait distributions across various sampling scenarios, taxa and datasets by comparing estimates derived from simulated samples with the true values calculated from full datasets. Simulations differ in sampling intensity (individuals per species), sampling biases (abundance, size), trait data source (local vs. global) and estimation method (two types of community‐weighting, two types of bootstrapping). We introduce the traitstrap R package, which contains a modular and extensible set of bootstrapping and weighted‐averaging functions that use community composition and trait data to estimate the moments of community trait distributions with their uncertainty. Importantly, the first function in the workflow, trait_fill , allows the user to specify hierarchical structures (e.g. plot within site, experiment vs. control, species within genus) to assign trait values to each taxon in each community sample. Across all taxa, simulations and metrics, bootstrapping approaches were more accurate and less biased than community‐weighted approaches. With bootstrapping, a sample size of 9 or more measurements per species per trait generally included the true mean within the 95% CI. It reduced average percent errors by 26%–74% relative to community‐weighting. Random sampling across all species outperformed both size‐ and abundance‐biased sampling. Our results suggest randomly sampling ~9 individuals per sampling unit and species, covering all species in the community and analysing the data using nonparametric bootstrapping generally enable reliable inference on trait distributions, including the central moments, of communities. By providing better estimates of community trait distributions, bootstrapping approaches can improve our ability to link traits to both the processes that generate them and their effects on ecosystems.

Maitner, Brian S.↗

DOE OSTI2020

A Bayesian Approach to Regional Decadal Predictability: Sparse Parameter Estimation in High-Dimensional Linear Inverse Models of High-Latitude Sea Surface Temperature Variability

Stochastic reduced models are an important tool in climate systems whose many spatial and temporal scales cannot be fully discretized or underlying physics may not be fully accounted for. One form of reduced model, the linear inverse model (LIM), has been widely used for regional climate predictability studies—typically focusing more on tropical or midlatitude studies. However, most LIM fitting techniques rely on point estimation techniques deriving from fluctuation–dissipation theory. In this methodological study we explore the use of Bayesian inference techniques for LIM parameter estimation of sea surface temperature (SST), to quantify the skillful decadal predictability of Bayesian LIM models at high latitudes. We show that Bayesian methods, when compared to traditional point estimation methods for LIM-type models, provide better calibrated probabilistic skill, while simultaneously providing better point estimates due to the regularization effect of the prior distribution in high-dimensional problems. We compare the effect of several priors, as well as maximum likelihood estimates, on 1) estimating parameter values on a perfect model experiment and 2) producing calibrated 1-yr SST anomaly forecast distributions using a preindustrial control run of the Community Earth System Model (CESM). Finally, we employ a host of probabilistic skill metrics to determine the extent to which an LIM can forecast SST anomalies at high latitudes. We find that the choice of prior distribution has an appreciable impact on estimation outcomes, and priors that emphasize physically relevant properties enhance the model’s ability to capture variability of SST anomalies.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Forced Component Estimation Statistical Method Intercomparison Project (ForceSMIP)

Anthropogenic climate change is unfolding rapidly, yet its regional manifestation can be obscured by internal variability. A primary goal of climate science is to identify the externally forced climate response from among the noise of internal variability. Separating the forced response from internal variability can be addressed in climate models by using a large ensemble to average over different possible realizations of internal variability. However, with only one realization of the real world, it is a major challenge to isolate the forced response directly in observations. In the Forced Component Estimation Statistical Method Intercomparison Project (ForceSMIP), contributors used existing and newly developed statistical and machine learning methods to estimate the forced response over 1950–2022 within individual realizations of the climate system. Participants used neural networks, linear inverse models, fingerprinting methods, and low-frequency component analysis, among other approaches. These methods were trained using large ensembles from multiple climate models and then applied to observations. Here, we evaluate method performance within large ensembles and investigate the estimates of the forced response in observations. Our results show that many different types of methods are skillful for estimating the forced response in climate models, though the relative skill of individual methods varies depending on the variable and evaluation metric. Methods with comparable skill in models can give a wide range of estimates of the forced response pattern in observations, illustrating the epistemic uncertainty in forced response estimates. ForceSMIP gives new insights into the forced response in observations, its uncertainty, and methods for its estimation.

Climate attribution↗

DOE OSTI2024

How robust are estimates of key parameters in standard viral dynamic models?

Mathematical models of viral infection have been developed, fitted to data, and provide insight into disease pathogenesis for multiple agents that cause chronic infection, including HIV, hepatitis C, and B virus. However, for agents that cause acute infections or during the acute stage of agents that cause chronic infections, viral load data are often collected after symptoms develop, usually around or after the peak viral load. Consequently, we frequently lack data in the initial phase of viral growth, i.e., when pre-symptomatic transmission events occur. Missing data may make estimating the time of infection, the infectious period, and parameters in viral dynamic models, such as the cell infection rate, difficult. However, having extra information, such as the average time to peak viral load, may improve the robustness of the estimation. Here, we evaluated the robustness of estimates of key model parameters when viral load data prior to the viral load peak is missing, when we know the values of some parameters and/or the time from infection to peak viral load. Although estimates of the time of infection are sensitive to the quality and amount of available data, particularly pre-peak, other parameters important in understanding disease pathogenesis, such as the loss rate of infected cells, are less sensitive. Viral infectivity and the viral production rate are key parameters affecting the robustness of data fits. Fixing their values to literature values can help estimate the remaining model parameters when pre-peak data is missing or limited. We find a lack of data in the pre-peak growth phase underestimates the time to peak viral load by several days, leading to a shorter predicted growth phase. On the other hand, knowing the time of infection (e.g., from epidemiological data) and fixing it results in good estimates of dynamical parameters even in the absence of early data. While we provide ways to approximate model parameters in the absence of early viral load data, our results also suggest that these data, when available, are needed to estimate model parameters more precisely.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Estimating time in quantum chaotic systems and black holes

We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation". Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time values. Intuitively, it should become increasingly difficult to estimate the precise value of time by making measurements on the state. We use a quantity called the Fisher information from quantum metrology to quantify the minimum uncertainty in estimating time. Due to unitarity, the uncertainty in the time estimate does not grow with time if we have access to optimal measurements on the full system. Restricting the measurements to act on a small subsystem or to have low computational complexity leads to results expected from equilibration, where the time uncertainty becomes large at late times. With optimal measurements on a subsystem larger than half of the system, we regain the ability to estimate the time very precisely, even at late times. Hawking's calculation for the reduced density matrix of the black hole radiation in semiclassical gravity contradicts our general predictions for unitary quantum chaotic systems. Hawking's state always has a large uncertainty for attempts to estimate the time using the radiation, whereas our general results imply that the uncertainty should become small after the Page time. This gives a new version of the black hole information loss paradox in terms of the time estimation task. By restricting to simple measurements on the radiation, the time uncertainty becomes large. This indicates from a new perspective that the observations of computationally bounded agents are consistent with the semiclassical effective description of gravity.

Black holes↗

DOE OSTI2021

Surrogate Modeling For Efficiently Accurately and Conservatively Estimating Measures of Risk

We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. We adopt a probabilistic description of risk that assigns probabilities to consequences associated with an event and use risk measures, which combine objective evidence with the subjective values of decision makers, to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical estimates obtained from the training data. These surrogate models not only limit over-confidence in reliability and safety assessments, but produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to the specific risk preferences of the stakeholder and then present an approach, based upon stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. The surrogate models introduce a bias that allows them to conservatively estimate the target risk measures. We provide theoretical results that show that this bias decays at the same rate as the L 2 error in the surrogate model. Our numerical examples confirm that risk-aware surrogate models do indeed over-estimate the target risk measures while converging at the expected rate.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Quantifying Uncertainty in PV Energy Estimates Final Report

Uncertainty in PV energy estimates is "one of the most critical areas of lack of understanding" according to independent engineers, financiers, PV model developers, and other industry stakeholders. The primary problem is a lack of rigorous, transparent, widely accepted methods for quantifying uncertainty in energy production estimates. Uncertainty in energy production estimates arises from variability of the solar resource, inexact PV performance models and their parameters, and system reliability considerations. Uncertainty in annual energy production is frequently calculated for larger projects in order to quantify financial risk. Key statistics for energy, such as the P-values "P50" and "P90" (the annual energy values that are exceeded in future years with 50\% and 90\% probability, respectively) are used by financing institutions to calculate the repayment risk for the project. The current methods to estimate these statistics are typically proprietary, specialized, and involve significant post-processing of commercial performance model results. This black-box approach leads to inconsistent P-value estimates from different parties, which reduces investors' confidence in the results. Since the financial community bases its risk assessment on these estimates, reduced confidence increases perceived project risk, and consequently financing costs. The goal of this project was to establish a set of best practices for quantifying uncertainty in energy production estimates, including identifying what sources of uncertainty must be considered with clear definitions and metrics, determining which sources are the biggest drivers of uncertainty, and providing a computationally efficient framework for combining different sources of uncertainty that is flexible enough to accommodate substitutions of data or methods when better information is available. We engaged a wide set of stakeholders to ensure industry endorsement and adoption, and leveraged complementary projects investigating individual sources of uncertainty in great detail, as well as others' work that started down this path.

ENERGY PLANNING, POLICY, AND ECONOMY,SOLAR ENERGY↗

DOE OSTI2024

Commercial, industrial, and institutional discount rate estimation for efficiency standards analysis: Sector-level data 1998–2023

Underlying each of the U.S. Department of Energy’s (DOE’s) federal appliance and equipment energy conservation standards are a set of complex analyses of the projected costs and benefits of regulation. Any new or amended standard must be designed to achieve significant additional energy conservation, provided that it is technologically feasible and economically justified (42 U.S.C. 6295(o)(2)(A)). DOE determines economic justification based on whether the benefits exceed the burdens, considering a variety of factors, including the economic impact of the standard on consumers of the product and the savings in lifetime operating cost compared to any increase in price or maintenance expenses (42 U.S.C. 6295(o)(2)(B)). As part of this determination, DOE conducts a life-cycle cost (LCC) analysis, which models the combined impact of appliance first cost and operating cost changes on a representative commercial building sample to identify the fraction of customers achieving LCC savings or incurring net cost at the considered efficiency levels. Thus, the commercial discount rate value(s) used to calculate the present value of energy cost savings within the LCC model implicitly plays a role in estimating the economic impact of potential standard levels. This report provides an in-depth discussion of the commercial discount rate estimation process relying on the Capital Asset Pricing Model (CAPM) to estimate a business’ cost of equity, and by adding a risk adjustment factor to the risk-free rate associated with long-term U.S. Treasury bonds to estimate their cost of debt. It is an update to previous reports on estimating commercial discount rates from firm-level and sector-level financial data (e.g., Fujita, 2021, 2016). Major topics covered in this report include the following: • Discount rate estimation methods and rationale • Data sources used and data limitations • Discount rate distributions for use in standards analysis • Discount rate estimation methods and distributions specific to the small business subgroup analysis.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗